Electrical device degradation determination

ABSTRACT

A method collects from at least one power measuring device of an environment power consumption data indicating active power consumption during a timeframe by an electrical device in the environment. The method also collects operating parameter data indicating at least one operating parameter under which the electrical device operates during at least a portion of the timeframe. The method performs, based on observing an increase in power consumption of the electrical device during the timeframe, assessing extents of contribution by potential contributing factors to the increase in power consumption, the potential contributing factors including time-based degradation of the electrical device and the at least one operating parameter. The method outputs, based on the assessing, an indication of an extent of contribution of degradation of the electrical device to the increase in power consumption.

BACKGROUND

Electrical devices, for instance home appliances such as heating andcooling equipment, undergo energy consumption performance degradationover time as the devices are used. There may be several differentparameters that affect the rate and extent of this degradation, howeverexisting approaches for monitoring energy efficiency performance fail toprovide a comprehensive framework that adequately and properly considersthese parameters.

SUMMARY

Shortcomings of the prior art are overcome and additional advantages areprovided through the provision of a computer-implemented method. Themethod collects from at least one power measuring device of anenvironment power consumption data indicating active power consumptionduring a timeframe by an electrical device in the environment. Themethod also collects operating parameter data indicating at least oneoperating parameter under which the electrical device operates during atleast a portion of the timeframe. The method performs, based onobserving an increase in power consumption of the electrical deviceduring the timeframe, assessing extents of contribution by potentialcontributing factors to the increase in power consumption, the potentialcontributing factors including time-based degradation of the electricaldevice and the at least one operating parameter. The method outputs,based on the assessing, an indication of an extent of contribution ofdegradation of the electrical device to the increase in powerconsumption.

Further, a computer program product including a computer readablestorage medium readable by a processor and storing instructions forexecution by the processor is provided for performing a method. Themethod collects from at least one power measuring device of anenvironment power consumption data indicating active power consumptionduring a timeframe by an electrical device in the environment. Themethod also collects operating parameter data indicating at least oneoperating parameter under which the electrical device operates during atleast a portion of the timeframe. The method performs, based onobserving an increase in power consumption of the electrical deviceduring the timeframe, assessing extents of contribution by potentialcontributing factors to the increase in power consumption, the potentialcontributing factors including time-based degradation of the electricaldevice and the at least one operating parameter. The method outputs,based on the assessing, an indication of an extent of contribution ofdegradation of the electrical device to the increase in powerconsumption.

Yet further, a computer system is provided that includes a memory and aprocessor in communications with the memory, wherein the computer systemis configured to perform a method. The method collects from at least onepower measuring device of an environment power consumption dataindicating active power consumption during a timeframe by an electricaldevice in the environment. The method also collects operating parameterdata indicating at least one operating parameter under which theelectrical device operates during at least a portion of the timeframe.The method performs, based on observing an increase in power consumptionof the electrical device during the timeframe, assessing extents ofcontribution by potential contributing factors to the increase in powerconsumption, the potential contributing factors including time-baseddegradation of the electrical device and the at least one operatingparameter. The method outputs, based on the assessing, an indication ofan extent of contribution of degradation of the electrical device to theincrease in power consumption.

Additional features and advantages are realized through the conceptsdescribed herein.

BRIEF DESCRIPTION OF THE DRAWINGS

Aspects described herein are particularly pointed out and distinctlyclaimed as examples in the claims at the conclusion of thespecification. The foregoing and other objects, features, and advantagesof the invention are apparent from the following detailed descriptiontaken in conjunction with the accompanying drawings in which:

FIG. 1 depicts an example environment to incorporate and use aspectsdescribed herein;

FIGS. 2A and 2B collectively depict an example process for detectingtime-based degradation of a heating/cooling appliance based on powerconsumption patterns of active power, in accordance with aspectsdescribed herein;

FIG. 3 depicts an example process for electrical device degradationdetermination, in accordance with aspects described herein;

FIG. 4 depicts an example graph illustrating trends, by-month, in energyconsumed by an electrical device across multiple years;

FIGS. 5-10 depict data graphs from a simulated detection of time-baseddegradation of a heating/cooling appliance based on power consumptionpatterns of active power, in accordance with aspects described herein;

FIG. 11 depicts one example of a computer system and associated devicesto incorporate and/or use aspects described herein;

FIG. 12 depicts a cloud computing environment according to an embodimentof the present invention; and

FIG. 13 depicts abstraction model layers according to an embodiment ofthe present invention.

DETAILED DESCRIPTION

While developments have been made in monitoring energy efficiencyperformance of electrical equipment/devices, no comprehensive method andframework exists to check electrical equipment degradation thatconsiders the environmental and operating conditions or parameters andemploys statistical analysis, such as validation analysis, to separatethe impact of anomalous (outlier) power consumption due to abnormaloperating conditions. Described herein are aspects providing a unifiedframework and methodology to enable informed decision-making forcustomers and other stakeholders to increase energy savings when usingvarious electrical equipment. Aspects described herein can helpstakeholders detect degradation of an electrical device by monitoringits patterns of energy consumption of active power, also known as “real”power. Active/real power is contrasted to other expressions of power,such as reactive and apparent power.

Output can help stakeholders realize energy savings by way of repairingor replacing electrical equipment when degradation is found to beabnormal, even when the equipment is operating under anomalous orabnormal operating conditions. Aspects can use multivariate dataanalysis considering time-based degradation together with the impact ofvariables such as ambient temperature, humidity, and real/active powerconsumption, to detect equipment deterioration by various metrics, suchas peak monthly and average year-over-year active power consumption.

In particular, described herein is a method and framework that analyzeswhether an observed increase in power consumption is due to devicedegradation, as opposed to variation(s) in a number of operatingparameters of the electrical device, and the respective extents to whichthose variables contribute to the increase in power consumption. In thecase of home heating, ventilation and air conditioning (HVAC) equipment,operating parameters considered can include the temperature and/orhumidity under which the equipment operates, statuses of pertinentstructural features like doors and windows of the building, and/ornumber of occupants in the building, as examples, which can all affecthow much energy the equipment consumes in order to meet the desiredheating or cooling level. The impact of these anomalies, leading tospikes in consumption and outlier data, is considered and may be removedin comparing the equipment's consumption with historical consumptionvalues. In particular, if an increase in consumption is observed whencomparing to historical values, the increase may be due to devicedegradation, operating parameters such as temperature, humidity, etc.,and/or a combination of the foregoing. What might appear to be anabnormal rate of degradation of the device may actually be the result ofabnormal operating parameters that cause the device to consume aninordinate amount of energy. Conversely, an apparently efficientlyperforming electrical device may suffer from faster degradation that isnot observed because the operating parameters are particularly forgivingto the equipment. Aspects can further validate hypotheses withcomprehensive testing and/or multivariate analysis considering variousmetrics, such as the average time (based on historical consumption)during which the device has been switched on and both peak monthly andaverage monthly year-over-year comparison.

Accordingly, some features provided in accordance with aspects of thedescribed method/framework to detect presence and extent of degradationof, e.g., heating and cooling appliances based on power consumptionpatterns of real/active power are as follows:

-   -   Employing a model that considers environmental and operational        parameters of the appliances for the performance analysis;    -   Removing impact of the anomalies of increase/outliers for        parameters like temperature, humidity, and/or status of        doors/windows and room occupancy before comparing the        consumption with historical value(s);    -   Employing regression model for predicting consumption specific        to degradation (independent of anomalous operating parameters);        over a timeframe, for instance several years, predict a schedule        of energy consumption to show device owner or other stakeholder        what can be expected in terms of consumption in the future;    -   Validating hypothesis/hypotheses of device power performance        degradation with comprehensive testing and multivariate        analysis;    -   Accounting for average time (based on historical consumption)        during which the existing device has been switched on and both        peak monthly and average monthly year-over-year comparison;    -   Building a foundation for triggering a decision for        replacement/repair of the appliance, comparing its power        consumption performance with that of comparable segments, for        instance same/similar user profile segment, same/similar        appliance, same/similar model, and/or same/similar        specification, as examples.

FIG. 1 depicts an example environment to incorporate and use aspectsdescribed herein. Environment 100 includes a cloud facility 106 hostingvarious components that may be accessed across one or more network(s),for instance one or more local area networks and/or wide areas networks,for instance the internet. Components include a home energy monitoring(HEM)/sensor/weather data gateway 108, a consumption time-series/sensorevent database 110, weather data database 112, and analytics engine 114.Communications links shown as arrow lines extending between componentsshown in FIG. 1 include wired and/or wireless communications links, suchas wired and/or cellular, Wi-Fi, or other types of wireless connections.More generally, these communications links may be any appropriatewireless or wired communication link(s) for communicating data.

Various systems communicate with the components of cloud facility 106. Aweather system 104, for instance an external, internet-availableresource for providing weather data via a weather applicationprogramming interface (API), communicates with HEM gateway 108 toprovide weather data, for instance weather data pertaining to a usageenvironment in which an electrical device is used. An example usageenvironment is building 102, which may be a home, as one example. Theweather data pertaining to the home may be time-series/sequencedtemperature and humidity values of the environment (location) of thehome.

Building 102 includes electrical appliances 120, for instance heating,ventilation and air conditioning (HVAC) appliances that consume power,one or more plugin power meter(s) 122, and an in-home display (IHD)/HEMsystem 118 that communicates with the HEM gateway 108 to provideconsumption time-series data. Building also includes sensors 116 thatcommunicate with the HEM gateway 108 to provide sensor data.

Metering at each load point (electrical device, e.g. each appliance) canbe achieved through any one or more mechanisms, for instance by way of aplugin power meter (as shown in the example of FIG. 1), demand responsesensors, instrumenting with a circuit breaker, using nonintrusive loadmonitoring (NILM), and/or power or energy disaggregation. In the exampleof FIG. 1, plugin power meter(s) 122 provide time-series powerconsumption data for connected appliance(s). The time-series powerconsumption data may include timestamped data values obtainedperiodically over time. A date value for a given time (indicated by anassociated timestamp) can represent the amount of active power consumedby the appliance since a last reporting (e.g. last timestamped datavalue). In this regard, power consumption data may be providedperiodically, for instance daily. The power consumption data isintegrated to IHD/HEM system 118 having a HEM server, which can providethe time-series power consumption data to a meter data acquisitiongateway server (e.g. component 108) hosted in the cloud facility 106.

Component 108 also acquires event indications/data form various sensors116, for instance sensors to indicate door and window open/closedstatus, and current room occupancy (how many individuals are present inroom(s) or HVAC zones of the building). The gateway 108 pushes thetime-series power consumption data and sensor event data to database 110for storage. Gateway 108 also invokes weather APIs on the weather system104 to fetch weather data (e.g. temperature, humidity) for a desiredanalysis period for a location of interest, e.g. a geographic region orarea where building 102 is located. Gateway 108 stores this data to theweather data database 112.

Analytics engine 114 processes the time-series power consumption data,sensor event data, and weather data to carry out analytics describedherein, for instance described with reference to FIGS. 2A and 2B. Insome embodiments, this analysis is performed on anappliance-by-appliance basis. An appliance may be a major appliance suchas an air conditioning unit, furnace, or the like. Additionally oralternatively, data collected from individual appliances may beaggregated based on appliance type (for example all heating devicesin/of/for the building, all cooling devices in/of/for the building,etc.) to form aggregate data on which analysis is performed.

Visualization system 124 is, for instance, a computer system thatintegrates with the analytics engine 114 to display near real-time powerconsumption performance information graphs, relating this performanceinformation to historical power consumption data of a given appliance oracross an appliance type.

FIGS. 2A and 2B collectively depict an example process for detectingtime-based degradation of a heating/cooling appliance based on powerconsumption patterns of active power, in accordance with aspectsdescribed herein. In some examples, one or more aspects of FIGS. 2A and2B are performed by a computer system, such as a computer system that isor provides analytics engine 114. Additionally, as noted, in someexamples this process is performed on a device-by-device basis, i.e. foreach electrical device of potentially several in the building 102.

The process obtains data from meter/IHD device(s) (202) then parses andaggregates the data as necessary to remove outliers (204). Furtheraspects of this parsing/aggregating are described below under the Parse,Aggregate, and Remove Outliers section. The process analyzes the impactof temperature, humidity and energy consumption over multiple years(206). Although the time period used in examples describe herein areyears, the period of time could be any desired period, shorter or longerthan a year. Aspects of analysis 206 are described below under the TrendAnalysis section. The process continues with data preparation (208),including (i) identifying a warmest month per each year and comparingyear-over-year energy consumption for that peak month along withtemperature and humidity conditions; (ii) calculating an average monthlyenergy consumption, average temperature, and humidity for each year; and(iii) comparing (i) and (ii) on a year-over-year basis. Aspects of datapreparation 208 are described below under the Data Preparation section.Based on the data preparation, the process continues with aspectsdescribed below under the Analysis of Variance section. Specifically,the process determines whether there is an increasing trend of energyconsumption over the years (210). If not (210, N), it means there is no(or a negligible amount) of degradation seen with the appliance (212)and the process ends. Otherwise, if an increase in power consumptionduring the relevant timeframe (e.g. the multiple years) is observed(210, Y), the process continues with (in this example) a multivariateanalysis (214) for items (i) and (ii) of the data preparation 208. Aspart of this, different factor (operating parameter) combinations arecompared to identify the statistically significant variables.

Based on the analysis 214, the process determines (e.g. based on astatistical t- or f-value and confidence level) whether the analysisreflects an increase in energy due to time decay independent oftemperature and humidity for both peak-monthly and average readings(216). If so (216, Y), the process indicates that degradation of theappliance is positive for peak-month and average year (218). The processreflects ‘highest degradation’ and predicts future degradation using,e.g., linear regression (220), then ends. In this regard, it is notedthat this is not necessarily a reflection that the device is degradingfaster than normal or expected. Instead, it is an indication that time(aging) is the most statistically-significant variable or factor in thedegradation of the device.

If instead at 216 it is determined that the analysis does not reflect anincrease in energy due to time decay independent of temperature andhumidity for both peak-monthly and average readings (216, N), theprocess continues (to FIG. 2B) to determine (e.g. based on a statisticalt- or f-value and confidence level) whether the analysis reflectsdegradation independent of temperature and humidity for eitherpeak-month or average yearly consumption (222). If so (222, Y), theprocess indicates that degradation of the appliance is positive forpeak-month or average year (224). The process reflects ‘moderatedegradation’ and predicts future degradation (226), e.g. using linearregression, then ends. It is noted again that this is not necessarily areflection that the device is degrading faster than normal or expected.Instead, it is an indication that time (aging) is astatistically-significant variable or factor in the degradation of thedevice, together with other factor(s).

Otherwise, if at 222 it is determined that the analysis does not reflectdegradation independent of temperature and humidity for eitherpeak-month or average yearly consumption (222, N), the process continuesby reflecting lowest or no degradation (228) and ends. In this regard,it reflects that temperature and/or humidity are more significantcontributors to device degradation than aging of the device.

Parse, Aggregate & Removing Outliers:

The parsing, aggregation, and outlier removal can proceed as follows:

1. Let T be timestamp (e.g. day, month, year) of the active energyconsumed (kWh) since the last timestamped data value.

2. Let E be that active energy consumed (in kWh).

3. Separate timestamp for data, month, and year into separate columns.Remove the outlier timestamp data values based on data from sensors,e.g. when number of occupants in room, zone or building is sensed to berelatively high (relative to normal), when a window or door sensorindicates a window or door is open, thereby potentially stressing theheating or cooling appliance, etc. In other words, this identifies whatdata should be considered outliers on the basis that a window or doorwas open, or there was a surge of occupants in the building, asexamples, which would all reflect a spike in consumption but not due todevice degradation.

4. Obtain the ambient temperature of the environment (e.g. the outsideenvironment in which the building is located) from a resource such as aweather website. In other words, obtain temperature readings of theambient (outside) environment.

5. Group, by month, the energy consumed by the electrical device. Insome embodiments, devices are considered in aggregate by devicetype/class, e.g. air conditioning unit(s), heating units, etc., in whichcase the data may be aggregated by device type/class. Additionally oralternatively, in some embodiments the grouping by month means group theJanuary consumption across multiple years, February consumption acrossthe multiple years, etc.

6. For each year, calculate the peak monthly and monthly average energyconsumption.

Trend Analysis:

Trend Analysis is conducted by plotting points between energyconsumption month-over-month over multiple (e.g. 3-4) years andsimilarly the overall relation between temperature and energyconsumption month-over-month (over 3-4 years). This is also performedfor the relation between humidity and energy consumptionmonth-over-month.

FIG. 4 depicts an example graph illustrating trends, by-month, in energyconsumed by an electrical device across multiple (5) years. Linesindicated by reference numerals 402-424 are paired with the twelvemonths of the year as follows: 402—January; 404—February; 406—March;408—April; 410—May; 412—June; 414—July; 416—August; 418—September;420—October; 422—November; 424—December. The graph shows fluctuations inenergy consumed both (i) across months within a given year, and (ii)across years, for each given month.

FIG. 9 depicts a graph showing a trend in change of energy consumptionwith temperature across the multiple years. This shows that as timeacross years 1998 to 2002, the device generally consumes progressivelygreater energy, and there is a direct relationship to temperature thatholds across a range of temperatures spanning about 25 units to about 46units.

Data Preparation:

The data preparation prepares the data for the multivariate analysis. Toprovide a year-over-year comparison for a desired time period, the datacan be grouped as illustrated in the following table. This grouping isdone by month in this example, but grouping by other time periods, suchas by season, may be used.

Average Energy Average Ambient Consumption for Peak Month YearTemperature for month Month Mn (nth month of Y1 T1 e1(Mn, Y1) Year 1) Mn(nth month of Y2 T2 e2(Mn, Y2) Year 2) Mn (nth month of Y3 T3 e3(Mn, Y3)Year 3)

In the example above, the peak energy consumption in each year happensto be the same (nth) month each year, though in other examples the monthof peak consumption varies across the years. The average ambienttemperature for the month is determined based on daily averagetemperature across the month, as is the average energy consumption forthe peak month.

The following table depicts a creation of average monthly energyconsumption for a heating/cooling appliance across three years:

Average Monthly Energy Average Ambient Consumption for Respective YearTemperature for Year Years Y1 T1Y E1(Y1) Y2 T2Y E2(Y2) Y3 T3Y E3(Y3)

In the above table, T1Y is the average ambient temperature for that year(e.g. Y1). It is noted that if humidity readings were part of theseexamples, the table could have another column for H1Y, H2Y, and H3Y

Below is an example simulated dataset for year-over-year consumption inpeak month of July:

Average Average Year Month Energy Consumed Temperature Humidity 1 1998July 550 45.9 64 2 1999 July 570 43.0 54 3 2000 July 580 44.0 56 4 2001July 610 44.0 64 5 2002 July 590 46.0 65

The simulated dataset in the preceding table is reflected in FIG. 6,showing a graph of the average monthly energy consumption andtemperature for peak month July across years 1998-2002. Data pointsindicated by reference numerals 602-610 represent energy consumed(y-axis) in the given year (x-axis) and incorporate shading toillustrate average temperature for that year, i.e. 602—1998 (avg. Julytemp 45.9); 604—1999 (avg. July temp 43.0); 606—2000 (avg. July temp44.0); 608—2001 (avg. July temp 44.0; 610—2002 (avg. July temp 46.0).

FIG. 7 presents a graphical representation of year-over-year comparisonof average monthly consumption for peak month July, similar to FIG. 6,except with a regression line clearly showing that there is an increasein energy consumption for the device on a year-by-year basis.

Analysis of Variance (ANOVA):

An objective of the Analysis of Variance is to compare and analyzewhether there is an increase in, e.g., average monthly and/or peakmonth, active power consumption over the years and assess whether thisincrease is due to operating parameters, such as temperature and/orhumidity, and/or device degradation.

A process can perform the multivariate analysis after determining thatan increase in energy consumption over the years has been observed inthe first place. Referring to FIG. 2A, it is determined at 210 whetheran increase is observed and, if not, then it concludes that nodegradation is seen (212). Otherwise, the process performs themultivariate analysis (214), after confirming that an increase inconsumption was observed (210, Y). As part of the multivariate analysis,it can compare different factor combinations to determine which one ormore factors are statistically significant and the extent to whichfactors are correlated. In the examples described herein, themultivariate analysis indicates whether temperature, humidity, orpossibly both are statistically significant such that they havecontributed to the increase in energy consumption.

In an example methodology, a process performs a two-way analysis ofvariance (ANOVA) testing to reject or pass hypotheses for year-wiseenergy consumption and for warmest/coolest (e.g. peak) monthconsumption. Below are example hypotheses:

1. H₀—There is no impact of time on active energy consumption;

2. H₁—There is no impact of ambient temperature on active energyconsumption for that month;

3. H₂— There is no impact of either average ambient temperature or time;

4. H₃— There is no impact of humidity;

5. H₄— There is no impact either due to humidity or temperature or both.

Using 95% confidence level and using df(m,z) where m and z areindividual degrees of freedom, determine sum of square of EnergyConsumption.

Sum of Mean F- Square df Square score Sum of Square of Year p X Sum ofSquare of Temperature q Y Sum of Square within r Z Sum of Square of BothFactors t M

In case F-score of year is more than the table value, we can reject theH₀ hypothesis:

F square=Between Group Variability/Variance within group:

${{Between}\mspace{14mu} {group}\mspace{14mu} {Variability}} = {\sum\limits_{1}^{n}\; \frac{\left( {e_{iav} - E_{IAV}} \right)^{2}}{K - 1}}$

e_(iav) denotes mean for the data in the group

E_(IAV) denotes mean of all the data

(e_(ij))=value of i th observation jth group

K denotes the number of Group

Within Group Variability=Σ_(i=1) ^(k)Σ₁ ^(n)(e _(ij) −e _(av))²/(N−K)

Df(p,t)=X>Xo. We can reject the hypothesis moderate degradation ift-value for Ho>H1, else show low degradation.

The following table depicts example multivariate analysis results foryear-over-year peak monthly consumption:

Mean Df Sum Sq. Sq. F value Pr(>F) HumidLocation3$Year 1 1440.0 1440.031.779 .112 HumidLocation3$Average. 1 252.6 252.6 5.576 .255 TemperatureHumidLocation3$Average. 1 262.0 262.0 5.783 .251 Humidity Residuals 145.3 45.3

The following table depicts example multivariate analysis results foryear-over-year average monthly consumption:

Mean Df Sum Sq. Sq. F value Pr(>F) Humverage$Year 1 3519 3519 23.507.129 Humverage$Average.Temperature 1 130 130 .866 .523Humverage$Average.Humidity 1 155 155 1.037 .494 Residuals 1 150 150

In the above, the P value is least for year (first row), meaning arelatively significant cause of degradation is time (i.e. aging of thedevice), rather than temperature and humidity. Though not shown in thetables above, the analysis can also include an assessment of thecombination of temperature and humidity (like would be done for passingor rejecting H4 above).

Linear Regression Model for Future Predictability of Degradation:

Use Regression model to predict future degradation and calculate slopefor each independent variable and their importance from t test.

With historic data about the device's consumption and an indication thatthe device is degrading with age, linear regression (or any otherdesired statistical approach) is used to predict future consumption ofthe device. This refers to a schedule of predicted future degradationattributable to further time-based degradation of the device, providingthe customer with a sense of how the equipment is expected to degrade.The prediction can predict not only future degradation, but also acorrelated presumed energy consumption, and therefore the cost tooperate the equipment, based on the rate of degradation and predictedconsumption levels.

Using a linear regression model, the following mathematical equationscan be used to create & predict the monthly energy or monthly timeconsumed for future: e(future)=a+b*t, i.e. ‘Future energy is equal to afunction of a (intercept/constant) and b, the slope.

$\mspace{20mu} {b = {\frac{{\sum\limits_{i = 0}^{n}\; \left( {e,t} \right)} - \left( {\sum\limits_{1}\; {e{\sum\limits_{1}^{n}\; t}}} \right)}{{\sum\limits_{1}^{n}\; t^{2}} - \left( {\sum\limits_{1}^{n}\; t} \right)^{2}} = {s_{et}/s_{tt}}}}$${{total}\mspace{14mu} {Sum}\mspace{14mu} {of}\mspace{14mu} {Squares}} = {s_{e} = {{\sum\limits_{i}^{n}\; \left( {e_{i} - e_{av}} \right)^{2}} = {{{Sum}\mspace{14mu} {of}\mspace{14mu} {Error}} = {s_{E} = {\sum\limits_{i}^{n}\; \left( {e_{i} - e_{P}} \right)^{2}}}}}}$$\mspace{20mu} {{{Sum}\mspace{14mu} {of}\mspace{14mu} {Error}} = {{ss}_{tt} = {\sum\limits_{i}^{n}\left( {t_{i} - t_{av}} \right)^{2}}}}$$\mspace{20mu} {{ss}_{et} = {\sum\limits_{i}^{n}{\left( {t_{i} - t_{av}} \right)\left( {e_{i} - e_{av}} \right)}}}$  t_(av) = Average  t  value, e_(av) = mean  of  e  value  t_(i)-ith  value  of  t, e_(i) = i  the  value  of  e  a = y(mean) − bx(mean)y(mean) − bx(mean)$\mspace{20mu} {{{Error}\mspace{14mu} {of}\mspace{14mu} {intercept}} = \sqrt[s]{\frac{1}{n} + \frac{\overset{\_}{t_{av}^{2}}}{{ss}_{tt}}}}$$\mspace{20mu} {{{Error}\mspace{14mu} {of}\mspace{14mu} {slope}} = \frac{s}{\sqrt{{ss}_{xtt}}}}$$\mspace{20mu} {s = {\frac{s_{E}}{n - 2} = {{standard}\mspace{14mu} {Deviation}\mspace{14mu} {e(t)}}}}$Hypothesis  checking  for  Linear  regression  model − Null  hypothesis  slope = 0  Alternate  Hypothesis  H₀  not  equal  to  zero$\mspace{20mu} {{{Calculate}\mspace{14mu} {the}\mspace{14mu} t\mspace{14mu} {value}} = {{\frac{r\sqrt{n - 2}r\sqrt{n - 2}}{\sqrt{1 - r^{2}}\sqrt{1 - r^{2}}}.\mspace{79mu} {Calculate}}\mspace{14mu} {the}\mspace{14mu} t\text{-}{value}{\; \;}{to}\mspace{14mu} {check}\; {if}\mspace{14mu} {regression}\mspace{14mu} {model}}}\mspace{11mu}$     slope  is  correct.  Hence, average  time  taken  by  the     degraded  equipment = e(t)/Power   Hence  tn = a + bt

Using the above linear regression model—calculate the final (energyconsumed for device) analysis:

e(t)=a+b(t)

E=Energy consumed as a function of time (years) (based on equipment'slinear data)

t=time consumed

Levels of Degradation:

The table below presents a comparison of levels of degradation based onthe multivariate ANOVA testing. In other words, each of the rowsrepresents a respective different scenario of passing/failinghypotheses. F1 represents degradation due to time, F2 representsdegradation due to temperature, and F3 represents degradation due tohumidity. This table may be specific to the peak month analysis, averagemonthly analysis, or an aggregate of both. In this example, whether agiven hypotheses passes is based on a configurable aggregation of (i)the analysis of average monthly consumption data, (ii) the analysis ofpeak monthly consumption data, and (iii) t-Test of Linear Regressionmodel for Computing Energy Consumption using Monthly average for eachyear. Note that in t-test there are 3 dependent variables—Year,Temperature and Humidity, and hence H3,H4,H5,H6 would not be valid.

H0 H1 H2 H3 H4 H5 H6 F1 F2 F3 F1*F2 F1*F3 F2*F3 F1*F2*F3 Result TestReject Pass Pass Pass Pass Pass Pass Strong candidate Results fordegradation Test Reject Pass Pass Pass Reject Pass Reject Strongcandidate Results for degradation Test Reject Pass Pass Pass Reject PassPass Strong candidate Results for degradation Test Reject Reject PassPass Pass Pass Reject Moderate Results Degradation Test Reject RejectPass Reject Pass Pass Reject Moderate Results degradation if t- valuefor H₀ > H₁, else show degradation Test Reject Reject Pass Reject PassPass Reject Moderate Results Degradation Test Pass Pass/ Pass/ Pass/Pass/ Pass/ Pass/ Low degradation Results Reject Reject Reject RejectReject Reject

As an example, the Analysis of Variance may indicate the scenario of thefirst row in the table above, in which H₀ is rejected but H₁ to H₆ allpass. The particular appliance being assessed in that case is deemed tobe a strong candidate for degradation (based on average and peak monthlyconsumption), meaning aging of the device has a statisticallysignificant impact on the increase in energy consumption.

The following presents an example simulated dataset and correspondingcalculations and output of the model using ‘R.’ (an open sourceprogramming language and software environment for statisticalcomputing), according to aspects described herein:

[[BEGIN SIMULATION]]

setwd(“˜/Research/DIR”)

HumidLocation<-read.csv(“˜/Research/DIR/HumidLocation.csv”)

View(HumidLocation)

library(dplyr)

## Attaching package: ‘dplyr’

## The following objects are masked from ‘package:stats’:

##

## filter, lag

## The following objects are masked from ‘package:base’:

##

## intersect, setdiff, setequal, union

library(tidyr)

library(ggplot2)

boxplot(HumidLocation$Energy.Consumed˜HumidLocation$Year)

[Refer to FIG. 5 for output.]

HumidLocation2<-HumidLocation %>% filter(Average.Temperature>41&Average.Humidity>50)

print(HumidLocation2)

Energy. Average. ## Year Month Consumed Temperature Average.Humidity ##1 1998 June 500 45.6 66 ## 2 1998 July 550 45.9 64 ## 3 1999 July 57043.0 54 ## 4 2000 July 580 44.0 56 ## 5 2001 July 610 44.0 64 ## 6 2002July 590 46.0 65

HumidLocation3<-HumidLocation2%>% filter(Month==‘July’)

print(HumidLocation3)

Energy. Average. ## Year Month Consumed Temperature Average.Humidity ##1 1998 July 550 45.9 64 ## 2 1999 July 570 43.0 54 ## 3 2000 July 58044.0 56 ## 4 2001 July 610 44.0 64 ## 5 2002 July 590 46.0 65

ggplot(HumidLocation3,aes(x=Year,y=Energy.Consumed,col=Average.Temperature))+geom_point( )

[Refer to FIG. 6 for output.]

# Considering Time, Temperature & humidity as Categorical variable andcomparing means in each category for each Month & Variance in theirgroup

av3<-aov(HumidLocation3$Energy.Consumed˜HumidLocation3$Year+HumidLocation3$Average.Temperature+HumidLocation3$Average.Humidity)

summary(av3)

## Df Sum Sq Mean Sq F value Pr (>F) ## HumidLocation3$Year 1 1440.01440.0 31.779 0.112 ## HumidLocation3$Average.Temperature 1 252.6 252.65.576 0.255 ## HumidLocation3$Average.Humidity 1 262.0 262.0 5.783 0.251## Residuals 1 45.3 45.3

model.tables(av3,“means”)

## Warning in replications(paste(“˜”, xx), data=mf): non-factorsignored:

## HumidLocation3$Year

## Warning in replications(paste(“˜”, xx), data=mf): non-factorsignored:

## HumidLocation3$Average.Temperature

## Warning in replications(paste(“˜”, xx), data=mf): non-factorsignored:

## HumidLocation3$Average.Humidity

## Tables of means

## Grand mean

##

##580

##

## HumidLocation3$Year

## HumidLocation3$Year

##1998 1999 2000 2001 2002

##556 568 580 592 604

##

## HumidLocation3$Average.Temperature

## HumidLocation3$Average.Temperature

##43 44 45.9 46

##588.9 583.9 570.5 572.8

##

## HumidLocation3 $Average.Humidity

## HumidLocation3$Average.Humidity

##54 56 64 65

##577.1 571.7 587.8 575.5

# Creating Average Data for the year and average time spent per year perdevice

Humverage<-HumidLocation %>% group_by(Year) % >%summarize_each(funs(mean),Energy. Consumed, Average.Temperature,Average.Humidity)

Humverage

## # A tibble: 5×4

Year Energy Consumed Avg. Temp. Avg. Hhumidity <int> <dbl> <dbl> <dbl> 11998 344.1667 35.29167 47.00000 2 1999 364.5000 34.83333 43.83333 3 2000365.7500 34.91667 38.08333 4 2001 386.2500 34.41667 47.16667 5 2002427.0833 34.16667 53.91667

Timedataframe<-Humverage %>% select(Energy.Consumed) %>%mutate(time=Energy. Consumed/5)

TimeaverageHumidlocation<-left_join(Humverage, Timedataframe,by=“Energy.Consumed”)

TimeaverageHumidlocation

Year Energy Consumed Avg. Temp. Avg. Hhumidity time <int> <dbl> <dbl><dbl> <dbl> 1 1998 344.1667 35.29167 47.00000 68.83333 2 1999 364.500034.83333 43.83333 72.90000 3 2000 365.7500 34.91667 38.08333 73.15000 42001 386.2500 34.41667 47.16667 77.25000 5 2002 427.0833 34.1666753.91667 85.41667

#Comparing mean in each category of temperature, year, Humidity andtheir variance for Monthly Average for Each Year

av<-aov(Humverage$Energy.Consumed˜Humverage$Year+Humverage$Average.Temperature+Humverage$Average.Humidity)

summary(av)

## Df Sum Sq Mean Sq F value Pr(>F) ## Humverage$Year 1 3519 3519 23.5070.129 ## Humverage$Avg.Temp 1 130 130 0.866 0.523 ## Humverage$Avg.Hum 1155 155 1.037 0.494 ## Residuals 1 150 150

model.tables(av,“means”)

## Warning in replications(paste(“˜”, xx), data=mf): non-factorsignored:

## Humverage$Year

## Warning in replications(paste(“˜”, xx), data=mf): non-factorsignored:

## Humverage$Average.Temperature

## Warning in replications(paste(“˜”, xx), data=mf): non-factorsignored:

## Humverage$Average.Humidity

## Tables of means

## Grand mean

##

##377.55

##

## Humverage$Year

## Humverage$Year

##1998 1999 2000 2001 2002

##340.0 358.8 377.6 396.3 415.1

##

## Humverage$Average.Temperature

## Humverage$Average.Temperature

##34.166 . . . 34.4166 . . . 34.833 . . . 34.9166.

##378.7 379.4 384.6 369.0

##35.29166 . . .

##376.1

##

## Humverage$Average.Humidity

## Humverage$Average.Humidity

##38.0833 . . . 43.833 . . . 47 47.166 . . .

##372.0 372.0 385.0 375.5

##53.9166 . . .

##383.3

print(TimeaverageHumidlocation)

## # A tibble: 5×5

Year Energy Consumed Avg. Temp. Avg. Hhumidity time <int> <dbl> <dbl><dbl> <dbl> 1 1998 344.1667 35.29167 47.00000 68.83333 2 1999 364.500034.83333 43.83333 72.90000 3 2000 365.7500 34.91667 38.08333 73.15000 42001 386.2500 34.41667 47.16667 77.25000 5 2002 427.0833 34.1666753.91667 85.41667

print(Timedataframe)

## # A tibble: 5×2

Energy Consumed time <dbl> <dbl> 1 344.1667 68.83333 2 364.5000 72.900003 365.7500 73.15000 4 386.2500 77.25000 5 427.0833 85.41667

ggplot(HumidLocation3, aes(x=Year, y=Energy. Consumed,col=Average.Temperature))+geom_point()+stat_smooth(method=“lm”,col=“red”)

[Refer to FIG. 7 for output.]

diaplot<-ggplot(HumidLocation,aes(x=Average.Temperature, y=Energy.Consumed))

diaplot<-diaplot+geom_point(aes(col=Year))

diaplot

[Refer to FIG. 8 for output.]

diaplot+geom_smooth(aes(col=Year))

## ‘geom_smooth( )’ using method=‘loess’

[Refer to FIG. 9 for output.]

diaplot2<-ggplot(HumidLocation,aes(x=Year,y=Energy.Consumed))+geom_point()

diaplot2+geom_smooth(aes(col=Month))

[Refer to FIG. 4 for output.]

#Regression model for YoY Comparison and comparison with Temperature

par(mfrow=c(2,2))

mod2=lm(time˜Year+Average.Temperature+Average.Humidity,data=TimeaverageHumidlocation)

plot(mod 2)

## Warning in sqrt(crit*p*(1−hh)/hh): NaNs produced

## Warning in sqrt(crit*p*(1−hh)/hh): NaNs produced

[Refer to FIG. 10 for output]

summary(mod 2)

##

## Call:

## lm(formula=time˜Year+Average.Temperature+Average.Humidity,

## data=TimeaverageHumidlocation)

##

## Residuals:

##1 2 3 4 5

##−0.3710 0.8396 0.4654−1.9657 1.0317

##

## Coefficients:

Estimate Std. Error t value Pr (>|t|) (Intercept) −4890.1309 6176.1879−0.792 0.574 Year 2.5236 2.8973 0.871 0.544 Avg. Temp −2.7339 11.3382−0.241 0.849 Avg. Hum 0.2907 0.2855 1.018 0.494

## Residual standard error: 2.447 on 1 degrees of freedom

## Multiple R-squared: 0.9621, Adjusted R-squared: 0.8485

## F-statistic: 8.47 on 3 and 1 DF, p-value: 0.2462

[[END SIMULATION]]

Aspects described herein differ from mere appliance classification andpower consumption anomaly detection. For example, some approaches use anunsupervised approach to determine anomalies in power consumption byimputing missing data, computing frequency spectrum, dissimilarity, lowdimensional embedding and estimating normalized local density. In otherexamples, power consumption anomalies are identified through differencesbetween real and predicted consumption by applying the two-sigma rule.In contrast, aspects described herein identify anomalies and comparewhether, and an extent to which, an increase in power consumption is dueto device degradation, as opposed to/in conjunction with variation in anumber of operating parameters like temperature, humidity, ordoor/window open status, number of occupants, etc. Additionally, aspectsdescribed herein can identify whether year-wise degradation exists forthe device using, e.g., two-way ANOVA testing. It can consider whetherhumidity and temperature, alone and in combination, have any impact onpeak month, year, or both, as independent factors or correlated factors(both temperature and humidity together) by performing multivariateanalysis. In case the null hypothesis is rejected, aspects can identifyestimated energy average consumed over some future timeframe for thedevice, using a linear regression model.

Accordingly, FIG. 3 depicts an example process for electrical devicedegradation determination, in accordance with aspects described herein.In some examples, the process is performed by one or more computersystems, such as those described herein, which may include one or morecomputer systems of or connected to an analytics engine, home energymonitoring system, and/or one of more other computer systems.

The process begins by collecting from at least one power measuringdevice of an environment, such as a geographic location or building atthat location, power consumption data indicating active powerconsumption during a timeframe by an electrical device in theenvironment (302). Example power measuring devices include meteringdevices, sensors, or the like installed in a building or home, asexamples. The electrical device can be an HVAC device, for instance ahome appliance providing heating, ventilation, and/or air conditioningfunctions.

The process also collects operating parameter data indicating at leastone operating parameter under which the electrical device operatesduring at least a portion of the timeframe (304). Example operatingparameters include local or ambient (i.e. outside of the building)weather conditions (such as temperature and/or humidity), status ofdoors/windows, and number of occupants in the environment/building, asexamples. Thus, the at least one operating parameter can include atleast one weather condition of the environment.

In some examples, the at least one operating parameter includes one ormore selected operating parameters that are selected from the groupconsisting of: open/closed status of one or more doors of the building,open/closed status of one or more windows of the building, and number ofoccupants in the building. Collecting the operating parameter data caninclude collecting the operating parameter data as sensor events fromone or more sensors installed in the building that sense the selectedone or more operating parameters.

In some examples, collecting the operating parameter data includescollecting at least some of the operating parameter data from aninternet-available resource that provides measurements of operatingparameters of the environment. For instance, weather data may beobtained via a weather API, or by harvesting it from a website.

Collecting the power consumption data and the operating parameter datacan in some examples include collecting at least some of the powerconsumption data and at least some of the operating parameter data froma computer system installed in the environment, for instance a HEMsystem that receives the at least some of the power consumption data andthe at least some of the operating parameter data from one or moresensors installed in the environment.

Continuing with the process of FIG. 3, based on observing an increase inpower consumption of the electrical device during the timeframe, theprocess assesses the extents of contribution by potential contributingfactors to the increase in power consumption (306). The potentialcontributing factors can include time-based degradation of theelectrical device and the at least one operating parameter for whichdata was collected. The assessing can consider contribution ofdegradation of the electrical device to the increase in powerconsumption independent of contribution of, e.g., the at least oneweather condition operating parameter(s) to the increase in powerconsumption.

The assessing can include eliminating at least one outlier from thepower consumption data based on the at least one outlier being a resultof an atypical operating parameter status of at least one of theselected one or more operating parameters. For instance, when the sensordata for the door/window/occupants indicates ‘atypical’ (e.g. windowopen, door open, large volume of occupants) and that status leads to anoutlier in power consumption for the relevant timeframe during which theabnormal status is present, that outlier data can be eliminated.

The process of FIG. 3 then outputs, based on the assessing, anindication of an extent of contribution of degradation of the electricaldevice to the increase in power consumption (308). In some examples,this output is to another computer system, for instance to avisualization system for a user to view.

This extent of contribution of degradation may be zero. Therefore, theprocess determines whether time-based degradation was found (310). Ifnot (310, N), then process ends. Otherwise (310, Y), the processproceeds to perform any of various desired actions (312). As an example,the process predicts and outputs a schedule of predicted futuretime-based degradation. For instance, the timeframe (during which themeasured active power consumption occurred) may be an initial timeframeand the process could perform predicting and outputting a schedule ofpredicted future degradation of the electrical device attributable tofurther electrical device degradation over a future timeframe, where thepredicting uses the assessed extent of contribution of degradation ofthe electrical device to the increase in power consumption during theinitial timeframe. Additionally or alternatively, the process couldascertain, based on the assessed extent of contribution of degradationof the electrical device to the increased power consumption, a level ofdegradation of the electrical device during the timeframe (meaning howmuch the device degraded during that time. If it degraded a significantamount, it may need to be replaced or repaired. The process could thencompare the ascertained level of degradation of the electrical device toan expected level of degradation of the electrical device expected tooccur during the timeframe. This expected level could be formed based ondata for a same/similar user profile segment, same/similar appliance,same/similar model and specification, etc. The process could thentrigger a decision for electrical device replacement or repair based onthe comparing indicating that the ascertained level of degradation ofthe electrical device is abnormal relative to the expected level ofdegradation. In other words, if the degradation of the device is higherthan average or at least some threshold, the process could alert a user,alert a device manufacture tor servicer, automatically reorder a part ofdevice, take any other desired actions.

In some examples, the assessing includes performing a statisticalanalysis based on hypotheses, where each hypothesis of the hypothesesincludes, as at least one variable of the hypothesis, a respective atleast one variable selected from the group consisting of: (i) an impactof time, and (ii) an impact of one or more operating parameters of theat least one operating parameter. Thus, each hypothesis can include one(or more) variables drawn from {impact of time, impact of one or more ofthe operating parameters that are being monitored}.

Based on an indication from the assessing that aging of the device has astatistically significant impact on the increase in energy consumptionindependent from any impact of any of the one or more operatingparameters, the outputting (308) can include indicating at least amoderate extent of contribution of degradation of the electrical devicedue to device aging. In other words, if aging is a factor independentfrom weather, etc., then the outputting can indicate moderate orpossibly high degradation. When the assessing considers both averagepeak-month power consumption of the electrical device across a number ofyears and average monthly consumption across the number of years, andbased on the assessing indicating, for both the average peak-month powerconsumption of the electrical device across the number of years andaverage monthly consumption across the number of years, that aging ofthe device has a statistically significant impact on the increase inenergy consumption independent from any impact of any of the one or moreoperating parameters, the outputting can include indicating a highextent of contribution of degradation of the electrical device due todevice aging. In other words, if aging is statistically significantindependent of weather, etc. and is found to be so across bothpeak-month over years and average monthly over year, then the level ofdegradation of the device due to aging may be reflected as ‘high’.

Based on an indication from the assessing that aging of the device doesnot have a statistically significant impact on the increase in energyconsumption independent from any impact of any of the one or moreoperating parameters, the outputting can include indicating at most alow extent of contribution of degradation of the electrical device dueto device aging. In this example, aging is not an independentlysignificant factor.

Although various examples are provided, variations are possible withoutdeparting from a spirit of the claimed aspects.

Processes described herein may be performed singly or collectively byone or more computer systems, such as one or more cloud servers, such asanalytics servers, and/or home energy monitoring systems, as examples.FIG. 11 depicts one example of such a computer system and associateddevices to incorporate and/or use aspects described herein. A computersystem may also be referred to herein as a data processingdevice/system, computing device/system/node, or simply a computer. Thecomputer system may be based on one or more of various systemarchitectures and/or instruction set architectures, such as thoseoffered by International Business Machines Corporation (Armonk, N.Y.,USA), Intel Corporation (Santa Clara, Calif., USA) or ARM Holdings plc(Cambridge, England, United Kingdom), as examples.

FIG. 11 shows a computer system 1100 in communication with externaldevice(s) 1112. Computer system 1100 includes one or more processor(s)1102, for instance central processing unit(s) (CPUs). A processor caninclude functional components used in the execution of instructions,such as functional components to fetch program instructions fromlocations such as cache or main memory, decode program instructions, andexecute program instructions, access memory for instruction execution,and write results of the executed instructions. A processor 1102 canalso include register(s) to be used by one or more of the functionalcomponents. Computer system 1100 also includes memory 1104, input/output(I/O) devices 1108, and I/O interfaces 1110, which may be coupled toprocessor(s) 1102 and each other via one or more buses and/or otherconnections. Bus connections represent one or more of any of severaltypes of bus structures, including a memory bus or memory controller, aperipheral bus, an accelerated graphics port, and a processor or localbus using any of a variety of bus architectures. By way of example, andnot limitation, such architectures include the Industry StandardArchitecture (ISA), the Micro Channel Architecture (MCA), the EnhancedISA (EISA), the Video Electronics Standards Association (VESA) localbus, and the Peripheral Component Interconnect (PCI).

Memory 1104 can be or include main or system memory (e.g. Random AccessMemory) used in the execution of program instructions, storage device(s)such as hard drive(s), flash media, or optical media as examples, and/orcache memory, as examples. Memory 1104 can include, for instance, acache, such as a shared cache, which may be coupled to local caches(examples include L1 cache, L2 cache, etc.) of processor(s) 1102.Additionally, memory 1104 may be or include at least one computerprogram product having a set (e.g., at least one) of program modules,instructions, code or the like that is/are configured to carry outfunctions of embodiments described herein when executed by one or moreprocessors.

Memory 1104 can store an operating system 1105 and other computerprograms 1106, such as one or more computer programs/applications thatexecute to perform aspects described herein. Specifically,programs/applications can include computer readable program instructionsthat may be configured to carry out functions of embodiments of aspectsdescribed herein.

Examples of I/O devices 1108 include but are not limited to microphones,speakers, Global Positioning System (GPS) devices, cameras, lights,accelerometers, gyroscopes, magnetometers, sensor devices configured tosense light, proximity, heart rate, body and/or ambient temperature,blood pressure, and/or skin resistance, and activity monitors. An I/Odevice may be incorporated into the computer system as shown, though insome embodiments an I/O device may be regarded as an external device(1112) coupled to the computer system through one or more I/O interfaces1110.

Computer system 1100 may communicate with one or more external devices1112 via one or more I/O interfaces 1110. Example external devicesinclude a keyboard, a pointing device, a display, and/or any otherdevices that enable a user to interact with computer system 1100. Otherexample external devices include any device that enables computer system1100 to communicate with one or more other computing systems orperipheral devices such as a printer. A network interface/adapter is anexample I/O interface that enables computer system 1100 to communicatewith one or more networks, such as a local area network (LAN), a generalwide area network (WAN), and/or a public network (e.g., the Internet),providing communication with other computing devices or systems, storagedevices, or the like. Ethernet-based (such as Wi-Fi) interfaces andBluetooth® adapters are just examples of the currently available typesof network adapters used in computer systems (BLUETOOTH is a registeredtrademark of Bluetooth SIG, Inc., Kirkland, Wash., U.S.A.).

The communication between I/O interfaces 1110 and external devices 1112can occur across wired and/or wireless communications link(s) 1111, suchas Ethernet-based wired or wireless connections. Example wirelessconnections include cellular, Wi-Fi, Bluetooth®, proximity-based,near-field, or other types of wireless connections. More generally,communications link(s) 1111 may be any appropriate wireless and/or wiredcommunication link(s) for communicating data.

Particular external device(s) 1112 may include one or more data storagedevices, which may store one or more programs, one or more computerreadable program instructions, and/or data, etc. Computer system 1100may include and/or be coupled to and in communication with (e.g. as anexternal device of the computer system) removable/non-removable,volatile/non-volatile computer system storage media. For example, it mayinclude and/or be coupled to a non-removable, non-volatile magneticmedia (typically called a “hard drive”), a magnetic disk drive forreading from and writing to a removable, non-volatile magnetic disk(e.g., a “floppy disk”), and/or an optical disk drive for reading fromor writing to a removable, non-volatile optical disk, such as a CD-ROM,DVD-ROM or other optical media.

Computer system 1100 may be operational with numerous other generalpurpose or special purpose computing system environments orconfigurations. Computer system 1100 may take any of various forms,well-known examples of which include, but are not limited to, personalcomputer (PC) system(s), server computer system(s), such as messagingserver(s), thin client(s), thick client(s), workstation(s), laptop(s),handheld device(s), mobile device(s)/computer(s) such as smartphone(s),tablet(s), and wearable device(s), multiprocessor system(s),microprocessor-based system(s), telephony device(s), networkappliance(s) (such as edge appliance(s)), virtualization device(s),storage controller(s), set top box(es), programmable consumerelectronic(s), network PC(s), minicomputer system(s), mainframe computersystem(s), and distributed cloud computing environment(s) that includeany of the above systems or devices, and the like.

Aspects described herein may be incorporated into and/or use a cloudcomputing environment. It is to be understood that although thisdisclosure includes a detailed description on cloud computing,implementation of the teachings recited herein are not limited to acloud computing environment. Rather, embodiments of the presentinvention are capable of being implemented in conjunction with any othertype of computing environment now known or later developed.

Cloud computing is a model of service delivery for enabling convenient,on-demand network access to a shared pool of configurable computingresources (e.g. networks, network bandwidth, servers, processing,memory, storage, applications, virtual machines, and services) that canbe rapidly provisioned and released with minimal management effort orinteraction with a provider of the service. This cloud model may includeat least five characteristics, at least three service models, and atleast four deployment models.

Characteristics are as follows:

On-demand self-service: a cloud consumer can unilaterally provisioncomputing capabilities, such as server time and network storage, asneeded automatically without requiring human interaction with theservice's provider.

Broad network access: capabilities are available over a network andaccessed through standard mechanisms that promote use by heterogeneousthin or thick client platforms (e.g., mobile phones, laptops, and PDAs).

Resource pooling: the provider's computing resources are pooled to servemultiple consumers using a multi-tenant model, with different physicaland virtual resources dynamically assigned and reassigned according todemand. There is a sense of location independence in that the consumergenerally has no control or knowledge over the exact location of theprovided resources but may be able to specify location at a higher levelof abstraction (e.g., country, state, or datacenter).

Rapid elasticity: capabilities can be rapidly and elasticallyprovisioned, in some cases automatically, to quickly scale out andrapidly released to quickly scale in. To the consumer, the capabilitiesavailable for provisioning often appear to be unlimited and can bepurchased in any quantity at any time.

Measured service: cloud systems automatically control and optimizeresource use by leveraging a metering capability at some level ofabstraction appropriate to the type of service (e.g., storage,processing, bandwidth, and active user accounts). Resource usage can bemonitored, controlled, and reported providing transparency for both theprovider and consumer of the utilized service.

Service Models are as follows:

Software as a Service (SaaS): the capability provided to the consumer isto use the provider's applications running on a cloud infrastructure.The applications are accessible from various client devices through athin client interface such as a web browser (e.g., web-based email). Theconsumer does not manage or control the underlying cloud infrastructureincluding network, servers, operating systems, storage, or evenindividual application capabilities, with the possible exception oflimited user-specific application configuration settings.

Platform as a Service (PaaS): the capability provided to the consumer isto deploy onto the cloud infrastructure consumer-created or acquiredapplications created using programming languages and tools supported bythe provider. The consumer does not manage or control the underlyingcloud infrastructure including networks, servers, operating systems, orstorage, but has control over the deployed applications and possiblyapplication hosting environment configurations.

Infrastructure as a Service (IaaS): the capability provided to theconsumer is to provision processing, storage, networks, and otherfundamental computing resources where the consumer is able to deploy andrun arbitrary software, which can include operating systems andapplications. The consumer does not manage or control the underlyingcloud infrastructure but has control over operating systems, storage,deployed applications, and possibly limited control of select networkingcomponents (e.g., host firewalls).

Deployment Models are as follows:

Private cloud: the cloud infrastructure is operated solely for anorganization. It may be managed by the organization or a third party andmay exist on-premises or off-premises.

Community cloud: the cloud infrastructure is shared by severalorganizations and supports a specific community that has shared concerns(e.g., mission, security requirements, policy, and complianceconsiderations). It may be managed by the organizations or a third partyand may exist on-premises or off-premises.

Public cloud: the cloud infrastructure is made available to the generalpublic or a large industry group and is owned by an organization sellingcloud services.

Hybrid cloud: the cloud infrastructure is a composition of two or moreclouds (private, community, or public) that remain unique entities butare bound together by standardized or proprietary technology thatenables data and application portability (e.g., cloud bursting forloadbalancing between clouds).

A cloud computing environment is service oriented with a focus onstatelessness, low coupling, modularity, and semantic interoperability.At the heart of cloud computing is an infrastructure comprising anetwork of interconnected nodes. One such node is node 10 depicted inFIG. 16.

Computing node 10 is only one example of a suitable cloud computing nodeand is not intended to suggest any limitation as to the scope of use orfunctionality of embodiments of the invention described herein.Regardless, cloud computing node 10 is capable of being implementedand/or performing any of the functionality set forth hereinabove.

Referring now to FIG. 16, illustrative cloud computing environment 50 isdepicted. As shown, cloud computing environment 50 comprises one or morecomputing nodes 10 with which local computing devices used by cloudconsumers, such as, for example, smartphone or other mobile device 54A,desktop computer 54B, laptop computer 54C, and/or automobile computersystem 54N may communicate. Nodes 10 may communicate with one another.They may be grouped (not shown) physically or virtually, in one or morenetworks, such as Private, Community, Public, or Hybrid clouds asdescribed hereinabove, or a combination thereof. This allows cloudcomputing environment 50 to offer infrastructure, platforms and/orsoftware as services for which a cloud consumer does not need tomaintain resources on a local computing device. It is understood thatthe types of computing devices 54A-N shown in FIG. 16 are intended to beillustrative only and that computing nodes 10 and cloud computingenvironment 50 can communicate with any type of computerized device overany type of network and/or network addressable connection (e.g., using aweb browser).

Referring now to FIG. 17, a set of functional abstraction layersprovided by cloud computing environment 50 (FIG. 16) is shown. It shouldbe understood in advance that the components, layers, and functionsshown in FIG. 17 are intended to be illustrative only and embodiments ofthe invention are not limited thereto. As depicted, the following layersand corresponding functions are provided:

Hardware and software layer 60 includes hardware and softwarecomponents. Examples of hardware components include mainframes 61; RISC(Reduced Instruction Set Computer) architecture based servers 62;servers 63; blade servers 64; storage devices 65; and networks andnetworking components 66. In some embodiments, software componentsinclude network application server software 67 and database software 68.

Virtualization layer 70 provides an abstraction layer from which thefollowing examples of virtual entities may be provided: virtual servers71; virtual storage 72; virtual networks 73, including virtual privatenetworks; virtual applications and operating systems 74; and virtualclients 75.

In one example, management layer 80 may provide the functions describedbelow. Resource provisioning 81 provides dynamic procurement ofcomputing resources and other resources that are utilized to performtasks within the cloud computing environment. Metering and Pricing 82provide cost tracking as resources are utilized within the cloudcomputing environment, and billing or invoicing for consumption of theseresources. In one example, these resources may comprise applicationsoftware licenses. Security provides identity verification for cloudconsumers and tasks, as well as protection for data and other resources.User portal 83 provides access to the cloud computing environment forconsumers and system administrators. Service level management 84provides cloud computing resource allocation and management such thatrequired service levels are met. Service Level Agreement (SLA) planningand fulfillment 85 provide pre-arrangement for, and procurement of,cloud computing resources for which a future requirement is anticipatedin accordance with an SLA.

Workloads layer 90 provides examples of functionality for which thecloud computing environment may be utilized. Examples of workloads andfunctions which may be provided from this layer include: mapping andnavigation 91; software development and lifecycle management 92; virtualclassroom education delivery 93; data analytics processing 94;transaction processing 95; and degradation determination 96.

The present invention may be a system, a method, and/or a computerprogram product at any possible technical detail level of integration.The computer program product may include a computer readable storagemedium (or media) having computer readable program instructions thereonfor causing a processor to carry out aspects of the present invention.

The computer readable storage medium can be a tangible device that canretain and store instructions for use by an instruction executiondevice. The computer readable storage medium may be, for example, but isnot limited to, an electronic storage device, a magnetic storage device,an optical storage device, an electromagnetic storage device, asemiconductor storage device, or any suitable combination of theforegoing. A non-exhaustive list of more specific examples of thecomputer readable storage medium includes the following: a portablecomputer diskette, a hard disk, a random access memory (RAM), aread-only memory (ROM), an erasable programmable read-only memory (EPROMor Flash memory), a static random access memory (SRAM), a portablecompact disc read-only memory (CD-ROM), a digital versatile disk (DVD),a memory stick, a floppy disk, a mechanically encoded device such aspunch-cards or raised structures in a groove having instructionsrecorded thereon, and any suitable combination of the foregoing. Acomputer readable storage medium, as used herein, is not to be construedas being transitory signals per se, such as radio waves or other freelypropagating electromagnetic waves, electromagnetic waves propagatingthrough a waveguide or other transmission media (e.g., light pulsespassing through a fiber-optic cable), or electrical signals transmittedthrough a wire.

Computer readable program instructions described herein can bedownloaded to respective computing/processing devices from a computerreadable storage medium or to an external computer or external storagedevice via a network, for example, the Internet, a local area network, awide area network and/or a wireless network. The network may comprisecopper transmission cables, optical transmission fibers, wirelesstransmission, routers, firewalls, switches, gateway computers and/oredge servers. A network adapter card or network interface in eachcomputing/processing device receives computer readable programinstructions from the network and forwards the computer readable programinstructions for storage in a computer readable storage medium withinthe respective computing/processing device.

Computer readable program instructions for carrying out operations ofthe present invention may be assembler instructions,instruction-set-architecture (ISA) instructions, machine instructions,machine dependent instructions, microcode, firmware instructions,state-setting data, configuration data for integrated circuitry, oreither source code or object code written in any combination of one ormore programming languages, including an object oriented programminglanguage such as Smalltalk, C++, or the like, and procedural programminglanguages, such as the “C” programming language or similar programminglanguages. The computer readable program instructions may executeentirely on the user's computer, partly on the user's computer, as astand-alone software package, partly on the user's computer and partlyon a remote computer or entirely on the remote computer or server. Inthe latter scenario, the remote computer may be connected to the user'scomputer through any type of network, including a local area network(LAN) or a wide area network (WAN), or the connection may be made to anexternal computer (for example, through the Internet using an InternetService Provider). In some embodiments, electronic circuitry including,for example, programmable logic circuitry, field-programmable gatearrays (FPGA), or programmable logic arrays (PLA) may execute thecomputer readable program instructions by utilizing state information ofthe computer readable program instructions to personalize the electroniccircuitry, in order to perform aspects of the present invention.

Aspects of the present invention are described herein with reference toflowchart illustrations and/or block diagrams of methods, apparatus(systems), and computer program products according to embodiments of theinvention. It will be understood that each block of the flowchartillustrations and/or block diagrams, and combinations of blocks in theflowchart illustrations and/or block diagrams, can be implemented bycomputer readable program instructions.

These computer readable program instructions may be provided to aprocessor of a general purpose computer, special purpose computer, orother programmable data processing apparatus to produce a machine, suchthat the instructions, which execute via the processor of the computeror other programmable data processing apparatus, create means forimplementing the functions/acts specified in the flowchart and/or blockdiagram block or blocks. These computer readable program instructionsmay also be stored in a computer readable storage medium that can directa computer, a programmable data processing apparatus, and/or otherdevices to function in a particular manner, such that the computerreadable storage medium having instructions stored therein comprises anarticle of manufacture including instructions which implement aspects ofthe function/act specified in the flowchart and/or block diagram blockor blocks.

The computer readable program instructions may also be loaded onto acomputer, other programmable data processing apparatus, or other deviceto cause a series of operational steps to be performed on the computer,other programmable apparatus or other device to produce a computerimplemented process, such that the instructions which execute on thecomputer, other programmable apparatus, or other device implement thefunctions/acts specified in the flowchart and/or block diagram block orblocks.

The flowchart and block diagrams in the Figures illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods, and computer program products according to variousembodiments of the present invention. In this regard, each block in theflowchart or block diagrams may represent a module, segment, or portionof instructions, which comprises one or more executable instructions forimplementing the specified logical function(s). In some alternativeimplementations, the functions noted in the blocks may occur out of theorder noted in the Figures. For example, two blocks shown in successionmay, in fact, be executed substantially concurrently, or the blocks maysometimes be executed in the reverse order, depending upon thefunctionality involved. It will also be noted that each block of theblock diagrams and/or flowchart illustration, and combinations of blocksin the block diagrams and/or flowchart illustration, can be implementedby special purpose hardware-based systems that perform the specifiedfunctions or acts or carry out combinations of special purpose hardwareand computer instructions.

In addition to the above, one or more aspects may be provided, offered,deployed, managed, serviced, etc. by a service provider who offersmanagement of customer environments. For instance, the service providercan create, maintain, support, etc. computer code and/or a computerinfrastructure that performs one or more aspects for one or morecustomers. In return, the service provider may receive payment from thecustomer under a subscription and/or fee agreement, as examples.Additionally or alternatively, the service provider may receive paymentfrom the sale of advertising content to one or more third parties.

In one aspect, an application may be deployed for performing one or moreembodiments. As one example, the deploying of an application comprisesproviding computer infrastructure operable to perform one or moreembodiments.

As a further aspect, a computing infrastructure may be deployedcomprising integrating computer readable code into a computing system,in which the code in combination with the computing system is capable ofperforming one or more embodiments.

As yet a further aspect, a process for integrating computinginfrastructure comprising integrating computer readable code into acomputer system may be provided. The computer system comprises acomputer readable medium, in which the computer medium comprises one ormore embodiments. The code in combination with the computer system iscapable of performing one or more embodiments.

Although various embodiments are described above, these are onlyexamples. For example, computing environments of other architectures canbe used to incorporate and use one or more embodiments.

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting. As used herein, thesingular forms “a”, “an” and “the” are intended to include the pluralforms as well, unless the context clearly indicates otherwise. It willbe further understood that the terms “comprises” and/or “comprising”,when used in this specification, specify the presence of statedfeatures, integers, steps, operations, elements, and/or components, butdo not preclude the presence or addition of one or more other features,integers, steps, operations, elements, components and/or groups thereof.

The corresponding structures, materials, acts, and equivalents of allmeans or step plus function elements in the claims below, if any, areintended to include any structure, material, or act for performing thefunction in combination with other claimed elements as specificallyclaimed. The description of one or more embodiments has been presentedfor purposes of illustration and description, but is not intended to beexhaustive or limited to in the form disclosed. Many modifications andvariations will be apparent to those of ordinary skill in the art. Theembodiment was chosen and described in order to best explain variousaspects and the practical application, and to enable others of ordinaryskill in the art to understand various embodiments with variousmodifications as are suited to the particular use contemplated.

What is claimed is:
 1. A computer-implemented method comprising:collecting from at least one power measuring device of an environmentpower consumption data indicating active power consumption during atimeframe by an electrical device in the environment; collectingoperating parameter data indicating at least one operating parameterunder which the electrical device operates during at least a portion ofthe timeframe; based on observing an increase in power consumption ofthe electrical device during the timeframe, assessing extents ofcontribution by potential contributing factors to the increase in powerconsumption, the potential contributing factors comprising time-baseddegradation of the electrical device and the at least one operatingparameter; and outputting, based on the assessing, an indication of anextent of contribution of degradation of the electrical device to theincrease in power consumption.
 2. The method of claim 1, wherein the atleast one operating parameter comprises at least one weather conditionof the environment, wherein the assessing considers contribution ofdegradation of the electrical device to the increase in powerconsumption independent of contribution of the at least one weathercondition to the increase in power consumption, and wherein theelectrical device comprises a home appliance providing at least oneselected from the group comprising: heating, ventilation, and airconditioning.
 3. The method of claim 1, wherein the environmentcomprises a building, wherein the at least one operating parametercomprises one or more selected operating parameters selected from thegroup consisting of: open/closed status of one or more doors of thebuilding, open/closed status of one or more windows of the building, andnumber of occupants in the building, wherein collecting the operatingparameter data comprises collecting the operating parameter data assensor events from one or more sensors installed in the building thatsense the selected one or more operating parameters, and wherein theassessing comprises eliminating at least one outlier from the powerconsumption data based on the at least one outlier being a result of anatypical operating parameter status of at least one of the selected oneor more operating parameters.
 4. The method of claim 1, wherein theassessing comprises performing a statistical analysis based onhypotheses, wherein each hypothesis of the hypotheses includes, as atleast one variable of the hypothesis, a respective at least one variableselected from the group consisting of: (i) an impact of time, and (ii)an impact of one or more operating parameters of the at least oneoperating parameter.
 5. The method of claim 4, wherein based on anindication from the assessing that aging of the device has astatistically significant impact on the increase in energy consumptionindependent from any impact of any of the one or more operatingparameters, the outputting comprises indicating at least a moderateextent of contribution of degradation of the electrical device due todevice aging.
 6. The method of claim 5, wherein the assessing considersboth average peak-month power consumption of the electrical deviceacross a number of years and average monthly consumption across thenumber of years, and wherein based on the assessing indicating, for boththe average peak-month power consumption of the electrical device acrossthe number of years and average monthly consumption across the number ofyears, that aging of the device has a statistically significant impacton the increase in energy consumption independent from any impact of anyof the one or more operating parameters, the outputting comprisesindicating a high extent of contribution of degradation of theelectrical device due to device aging.
 7. The method of claim 4, whereinbased on an indication from the assessing that aging of the device doesnot have a statistically significant impact on the increase in energyconsumption independent from any impact of any of the one or moreoperating parameters, the outputting comprises indicating at most a lowextent of contribution of degradation of the electrical device due todevice aging.
 8. The method of claim 1, wherein the timeframe is aninitial timeframe and wherein the method further comprises predictingand outputting a schedule of predicted future degradation of theelectrical device attributable to further electrical device degradationover a future timeframe, the predicting using the assessed extent ofcontribution of degradation of the electrical device to the increase inpower consumption during the initial timeframe.
 9. The method of claim1, further comprising: ascertaining, based on the assessed extent ofcontribution of degradation of the electrical device to the increasedpower consumption, a level of degradation of the electrical deviceduring the timeframe; comparing the ascertained level of degradation ofthe electrical device to an expected level of degradation of theelectrical device expected to occur during the timeframe; and triggeringa decision for electrical device replacement or repair based on thecomparing indicating that the ascertained level of degradation of theelectrical device is abnormal relative to the expected level ofdegradation.
 10. The method of claim 1, wherein the collecting the powerconsumption data and the collecting the operating parameter datacomprises collecting at least some of the power consumption data and atleast some of the operating parameter data from a computer systeminstalled in the environment that receives the at least some of thepower consumption data and the at least some of the operating parameterdata from one or more sensors installed in the environment.
 11. Themethod of claim 1, wherein collecting the operating parameter datacomprises collecting at least some of the operating parameter data froman internet-available resource providing measurements of operatingparameters of the environment.
 12. A computer system comprising: amemory; and a processor in communications with the memory, wherein thecomputer system is configured to perform a method comprising: collectingfrom at least one power measuring device of an environment powerconsumption data indicating active power consumption during a timeframeby an electrical device in the environment; collecting operatingparameter data indicating at least one operating parameter under whichthe electrical device operates during at least a portion of thetimeframe; based on observing an increase in power consumption of theelectrical device during the timeframe, assessing extents ofcontribution by potential contributing factors to the increase in powerconsumption, the potential contributing factors comprising time-baseddegradation of the electrical device and the at least one operatingparameter; and outputting, based on the assessing, an indication of anextent of contribution of degradation of the electrical device to theincrease in power consumption.
 13. The computer system of claim 12,wherein the environment comprises a building, wherein the at least oneoperating parameter comprises at least one weather condition of theenvironment as well as one or more selected operating parametersselected from the group consisting of: open/closed status of one or moredoors of the building, open/closed status of one or more windows of thebuilding, and number of occupants in the building, wherein collectingthe operating parameter data comprises collecting the operatingparameter data as sensor events from one or more sensors installed inthe building that sense the selected one or more operating parameters,wherein the assessing comprises eliminating at least one outlier fromthe power consumption data based on the at least one outlier being aresult of an atypical operating parameter status of at least one of theselected one or more operating parameters and the assessing considerscontribution of degradation of the electrical device to the increase inpower consumption independent of contribution of the at least oneweather condition to the increase in power consumption, and wherein theelectrical device comprises a home appliance providing at least oneselected from the group comprising: heating, ventilation, and airconditioning.
 14. The computer system of claim 12, wherein the assessingcomprises performing a statistical analysis based on hypotheses, whereineach hypothesis of the hypotheses includes, as at least one variable ofthe hypothesis, a respective at least one variable selected from thegroup consisting of: (i) an impact of time, and (ii) an impact of one ormore operating parameters of the at least one operating parameter. 15.The computer system of claim 14, wherein the assessing considers bothaverage peak-month power consumption of the electrical device across anumber of years and average monthly consumption across the number ofyears, wherein based on an indication from the assessing that aging ofthe device has a statistically significant impact on the increase inenergy consumption independent from any impact of any of the one or moreoperating parameters and based on the assessing indicating, for both theaverage peak-month power consumption of the electrical device across thenumber of years and average monthly consumption across the number ofyears, that aging of the device has a statistically significant impacton the increase in energy consumption independent from any impact of anyof the one or more operating parameters, the outputting comprisesindicating a high extent of contribution of degradation of theelectrical device due to device aging.
 16. The computer system of claim12, wherein the method further comprises: ascertaining, based on theassessed extent of contribution of degradation of the electrical deviceto the increased power consumption, a level of degradation of theelectrical device during the timeframe; comparing the ascertained levelof degradation of the electrical device to an expected level ofdegradation of the electrical device expected to occur during thetimeframe; and triggering a decision for electrical device replacementor repair based on the comparing indicating that the ascertained levelof degradation of the electrical device is abnormal relative to theexpected level of degradation.
 17. A computer program productcomprising: a computer readable storage medium readable by a processorand storing instructions for execution by the processor for performing amethod comprising: collecting from at least one power measuring deviceof an environment power consumption data indicating active powerconsumption during a timeframe by an electrical device in theenvironment; collecting operating parameter data indicating at least oneoperating parameter under which the electrical device operates during atleast a portion of the timeframe; based on observing an increase inpower consumption of the electrical device during the timeframe,assessing extents of contribution by potential contributing factors tothe increase in power consumption, the potential contributing factorscomprising time-based degradation of the electrical device and the atleast one operating parameter; and outputting, based on the assessing,an indication of an extent of contribution of degradation of theelectrical device to the increase in power consumption.
 18. The computerprogram product of claim 17, wherein the environment comprises abuilding, wherein the at least one operating parameter comprises atleast one weather condition of the environment as well as one or moreselected operating parameters selected from the group consisting of:open/closed status of one or more doors of the building, open/closedstatus of one or more windows of the building, and number of occupantsin the building, wherein collecting the operating parameter datacomprises collecting the operating parameter data as sensor events fromone or more sensors installed in the building that sense the selectedone or more operating parameters, wherein the assessing compriseseliminating at least one outlier from the power consumption data basedon the at least one outlier being a result of an atypical operatingparameter status of at least one of the selected one or more operatingparameters and the assessing considers contribution of degradation ofthe electrical device to the increase in power consumption independentof contribution of the at least one weather condition to the increase inpower consumption, and wherein the electrical device comprises a homeappliance providing at least one selected from the group comprising:heating, ventilation, and air conditioning.
 19. The computer programproduct of claim 17, wherein the assessing comprises performing astatistical analysis based on hypotheses, wherein each hypothesis of thehypotheses includes, as at least one variable of the hypothesis, arespective at least one variable selected from the group consisting of:(i) an impact of time, and (ii) an impact of one or more operatingparameters of the at least one operating parameter, wherein theassessing considers both average peak-month power consumption of theelectrical device across a number of years and average monthlyconsumption across the number of years, wherein based on an indicationfrom the assessing that aging of the device has a statisticallysignificant impact on the increase in energy consumption independentfrom any impact of any of the one or more operating parameters and basedon the assessing indicating, for both the average peak-month powerconsumption of the electrical device across the number of years andaverage monthly consumption across the number of years, that aging ofthe device has a statistically significant impact on the increase inenergy consumption independent from any impact of any of the one or moreoperating parameters, the outputting comprises indicating a high extentof contribution of degradation of the electrical device due to deviceaging.
 20. The computer program product of claim 17, wherein the methodfurther comprises: ascertaining, based on the assessed extent ofcontribution of degradation of the electrical device to the increasedpower consumption, a level of degradation of the electrical deviceduring the timeframe; comparing the ascertained level of degradation ofthe electrical device to an expected level of degradation of theelectrical device expected to occur during the timeframe; and triggeringa decision for electrical device replacement or repair based on thecomparing indicating that the ascertained level of degradation of theelectrical device is abnormal relative to the expected level ofdegradation.